$A$ ladder is resting against a wall at an angle of $30^\circ$ with the wall. $A$ man is ascending the ladder at the rate of $3 \, ft/sec$. His rate of approaching the wall is:

The radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$ and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder in $\text{cm}^3\text{/min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$,is:

Let a kind of bacteria grow following the function $f(t) = t^4$,where $t$ is given in seconds. If the rate of growth of the bacteria after $t_0$ seconds is $4000 \text{ units/second}$,then $t_0 =$

$A$ rod $AB$,$13 \text{ feet}$ long,moves with its ends $A$ and $B$ on two perpendicular lines $OX$ and $OY$ respectively. When $A$ is $5 \text{ feet}$ from $O$,it is moving away at the rate of $3 \text{ feet/sec}$. At this instant,$B$ is moving at the rate of:

$A$ triangle has two fixed vertices $A(a, 0)$ and $B(0, b)$. Let its third vertex $C$ move along the line $x = y$. If $s$ is the area of triangle $ABC$, then $\frac{ds}{dx} =$

If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising is: